The 25th Amendment to the Constitution reads in relevant part:
Last Tuesday (2/26/2017), Former Pres. Obama gave a speech in which he declared Trump is unfit to serve.Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
Obama: Trump is 'unfit to serve as president' - LA Times
He's hardly alone in that assessment.
So, if this is true or could be true, what is the process of removal likely to look like?
The Democrats in Congress began examining this question two weeks ago.
Dem launches panel to review presidential removal procedures | TheHill
It's uncertain exactly what the procedure would be, as there has never been a POTUS forcibly removed under the 25th as unfit. There have been POTUSES who were physically unable to serve, and their VPs served as Acting President while they lingered, but clearly that was different. JFK, for example, did not die immediately after being shot, and for that brief time, Johnson was Acting President.
There's also the much thornier question of mental health. What standard would be used to measure the mental health of a POTUS in aid of determining whether he is no longer fit to serve? There are so many in the law: competent to handle his own affairs, competent to stand trial, legally insane, a danger to himself and others, and so on. None of them seems at all suitable for use in measuring the mental fitness of a POTUS.
This is not impeachment. That's simpler (procedurally) than this.